LCM of 705, 660, 678, 200, 617
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 705, 660, 678, 200, 617 with the LCM of Two or More Numbers Calculator. Here we are teaching you two different methods through which you can calculate the LCM of 705, 660, 678, 200, 617. So, keep reading to learn more.
Given numbers are 705,660,678,200,617
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 705,660,678,200,617 is 21627454200.
Find LCM of 705,660,678,200,617 with Prime Factorization
| 2 | 705, 660, 678, 200, 617 |
| 2 | 705, 330, 339, 100, 617 |
| 3 | 705, 165, 339, 50, 617 |
| 5 | 235, 55, 113, 50, 617 |
| 47, 11, 113, 10, 617 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 5 x 47 x 11 x 113 x 10 x 617 = 21627454200
Therefore, the lowest common multiple of 705,660,678,200,617 is 21627454200.
LCM formula is LCM(a1, a2, an) = (a1 x a2 x an)/{GCF(a1 x a2 x an) x common factors}
Firstly, we have to find the product of all the numbers.
705 x 660 x 678 x 200 x 617 = 38929417560000
Then, let us find the GCF of these five numbers. To do so, we have to list down the factors for each number and choose the highest factor that is in all of the lists.
705 : 1, 3, 5, 15, 47, 141, 235, 705
660 : 1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 110, 132, 165, 220, 330, 660
678 : 1, 2, 3, 6, 113, 226, 339, 678
200 : 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200
617 : 1, 617
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 705,660,678,200,617, is 1.
Now, the common factors can be found like this.
705:3x 5x 47
660:2x 2x 3x 5x 11
678:2x 3x 113
200:2x 2x 2x 5x 5
617:617
From this, we can see that the common factors because they appear for more than two numbers. So, just multiply them all together.
2x 2x 2x 3x 3x 5x 5 = 1800
Therefore, the value for common factors is 1800.
Now that we have all the elements of the formula, we can plug them in to calculate the LCM.
LCM(a1, a2, an) = (a1 x a2 x an)/{GCF(a1 x a2 x an) x common factors}
LCM = 38929417560000/(1x1800)
LCM = 38929417560000/1800
LCM = 21627454200
Thus, we can understand that the LCM of 705,660,678,200,617 is 21627454200.
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FAQs on LCM of 705, 660, 678, 200, 617
1. What is the LCM of 705, 660, 678, 200, 617?
Answer: LCM of 705, 660, 678, 200, 617 is 21627454200.
2. How to calculate the LCM of 705, 660, 678, 200, 617?
The LCM can be found using two methods. You can either use the LCM formula or the prime factorization method to calculate the LCM of 705, 660, 678, 200, 617.
3. What is the LCM formula?
The LCM formula is LCM(a1, a2, an) = (a1 x a2 x an)/{GCF(a1 x a2 x an) x common factors}.